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Some results for infinite server poisson queues

Published online by Cambridge University Press:  14 July 2016

Mark Brown  and
Sheldon M. Ross
Mark Brown
Affiliation:
Cornell University
Sheldon M. Ross
Affiliation:
University of California, Berkeley
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Extract

We consider a queueing model in which arrivals occur according to a non-homogeneous Poisson process in batches of varying size, and in which a customer is served immediately upon arrival by one of an infinite number of servers.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 604 - 611
Copyright
Copyright © Applied Probability Trust 

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References

[1] Brown, M. (1968) An invariance property of Poisson processes arising in traffic flow theory. Stanford University Technical Report. Google Scholar
[2] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. Wiley, New York.Google Scholar
[3] Karlin, S. (1966) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
[4] Pyke, R. (1958) On renewal processes related to type I and type II counter models. Ann. Math. Statist. 29, 737–754.Google Scholar
[5] Rao, , Sudarsana, J. (1966) An application of stationary point processes to queueing and textile research. J. Appl. Prob. 3, 231–246.CrossRefGoogle Scholar
[6] Riordan, J. (1962) Stochastic Service Systems. Wiley, New York.Google Scholar
[7] Shanbhag, D. N. (1966) On infinite server queues with batch arrivals. J. Appl. Prob. 3, 274–279.Google Scholar
[8] Takács, L. (1957) On certain sojourn time problems in the theory of stochastic processes. Acta Math. Acad. Sci. Hung. III, 169–191.Google Scholar
[9] Benes, V. E. (1965) Mathematical Theory of Connecting Networks and Telephone Traffic. Academic Press, New York.Google Scholar